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Photons and Schr odinger Cats: Quantum Optomechanics Lajos Di osi Wigner Center for Physics July 24, 2015


  1. Photons and Schr¨ odinger Cats: Quantum Optomechanics Lajos Di´ osi Wigner Center for Physics July 24, 2015 ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� m ������ ������ m ������� ������� ������ ������ Ψ (x)= ; Ψ (x)= m ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ? ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ 1 / 10

  2. Contents Fotonic facilities: largest, smallest 1 Expanding domain of quantum theory 2 Quantum theory of massive bodies? 3 Quantum theory of massive bodies? 4 Mechanical Schr¨ odinger Cat in lab 5 Quantum optomechanics 6 Quantum optomechanics — theory 7 Quantum optomechanics — laser cooling 8 Quantum optomechanics — mechanical Cat 9 10 Back to largest, smallest 2 / 10

  3. Abstract Quantum mechanics of massive mechanical motion produces paradoxical results. Schr¨ odinger drafted in 1935 how the quantum state of a live cat would in principle evolve into the superposition of the live and the dead. For half a century, preparation of massive objects in macroscopically different superpositions was practically impossible. Some speculated that such superpositions should be precluded by modified quantum mechanics. Meanwhile a tremendous development happened in a different field: quantum optics. Photons became the most trustable and flexible probes of quantum systems coupled to them. They became the probes of massive mechanical objects. In quantum optomechanics, a quantized oscillator weighting nanograms or even grams, is coupled to photons for double purpose: preparation and detection of controlled quantum state of the massive oscillator. In the forthcoming decade, optomechanical experiments running already in labs or planned in space may confirm the validity of quantum mechanics for massive objects. Or, alternatively, optomechanics may confirm if standard quantum mechanics gets violated in massive objects. 3 / 10

  4. Fotonic facilities: largest, smallest LIGO (Laser Interferometer Gravita- tional Wave Observatory) at Hanford, Washington State. Michelson interfer- ometer with two 4km arms, pumped by high power laser. Sketch of table top Michelson interfer- ometer, size about few cm’s, “pumped” by a single foton at a time, to test me- chanical Schr¨ odinger Cats. 1 / 10

  5. Expanding domain of quantum theory black body radiation atom, molecule electron condensed matter elektrodynamics nucleus elementary particles massive bodies/gravitation ? cosmology? information living material ? human consciousness ? 2 / 10

  6. Quantum theory of massive bodies? QM at large can be paradoxical: Schr¨ odinger’s Cat (1935) Lock a live cat and a poisoning mech- anism triggered when radioactive decay detected, all inside a black box. Switch off the mechanism at meantime, the cat is remains in superposition forever: Ψ = | alive � + | dead � . Unless you open the box and look at the cat, to cause wave function � | alive � collapse at random: | alive � + | dead � = ⇒ | dead � That’s standard QM extended for large objects! Make tractable physics! Change cat for a massive sphere, alive-or-dead for here-or-there : | alive � + | dead � − → | here � + | there � 3 / 10

  7. Quantum theory of massive bodies? Mechanical “Schr¨ odinger Cat”: large “catness” small “catness” m m Ψ (x)= ; Ψ (x)= m No evidences yet: Experiments: max. 10000 amu (2013) Theory: ambiguity of Cat’s Newton field (1981) Why don’t we see any “Cats” in Nature: Cats are masked by environmental noise (1970) Cats decay spontaneously by gravity-related noise (1986) ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� m ������ ������ m ������� ������� ������ ������ Ψ (x)= ; Ψ (x)= m ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ? ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ ������� ������� ������ ������ 4 / 10

  8. Mechanical Schr¨ odinger Cat in lab Preperation: extremely demanding for isolation from environmental noise cooling to µ K smart suspending, supporting, binding, trapping creation of distant here and there by interaction with an other Cat :) by many (controlled) interactions with microscopic systems Verification: extremely demanding for the point is interference between here and there can’t fly through double-slit, grating Light quanta helps! Optomechanics : thermal isolation, laser cooling, optical binding, trapping, controlled fotonic interactions, fotons map interference between here and there into detector counts, ... 5 / 10

  9. Quantum optomechanics Two end-mirrors form optical cavity, pumped by input laser beam ω 0 , excites nearest e.m. mode ω c = ω 0 − ∆ . Mirror on rhs is movable, vibrates like mechanical oscillator ω m , it is our massive object. Output laser beam encodes position of the rhs mirror. 6 / 10

  10. Quantum optomechanics — theory i) simple part (Open Q-systems) cavity e.m. mode = damped oscillator movable mirror = damped oscillator coupling = light pressure ii) less simple part (Input-output formalism) iii) difficult part (Q-monitoring theory) laser input beam = time-continuous measurement of periodic driving + vacuum the output beam fluctuations extraction of information on output beam = periodic position of movable mirror field + vacuum fluctuations 7 / 10

  11. Quantum optomechanics — laser cooling Laser cooling was invented for atoms (1978) It works for our vibrating mirror as well In optomechanics: many cooling methods Ground state cooling: mK if ω m ∼ MHz (2011); µ K if ω m ∼ kHz (????) Resolved side-band cooling : Laser ω 0 tuned below cavity ω c just by the mechanical ω m : ω 0 + ω m = ω c Input beam foton can become resonant with the cavity by stealing one energy quantum of the vibrating mirror. The opposite process is off-resonant and suppressed. So, energy flows from mechanical motion to cavity mode. Then cavity dissipates it to the environment. 8 / 10

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